Site-specific recombination of DNA is an essential event in many biological processes involving genomic rearrangements. Currently there is great interest in well-characterized site-specific recombination systems that can be used to target genes to specific locations on eukaryotic chromosomes in vivo. Two site-specific recombination systems that have been effective in these applications are the FIp system of S. cerevisiae and the Cre system of bacteriophage P1, both of which belong to the Int superfamily of site-specific recombinases. Because of their important biological roles and wide range of applications, it is important to understand the physical and chemical factors that govern the efficiency, product distribution, and target specificity of these recombination systems. We will develop a detailed understanding of the common features of the Int superfamily of site-specific recombinases using FIp, Cre, and lambda Int as model systems. We will investigate the respective structures of the synaptic complex, the intermediate nucleoprotein complex involved in recombination-site pairing and strand exchange, by using conventional and cryo-electron microscopy. Cryomicroscopy of tilted specimens will be used to generate stereo reconstructions of recombinase-DNA complexes, which will provide rigorous models for the geometry of DNA in each of the synaptic complexes. These biophysical studies will be carried out in conjunction with an analysis of the topology of recombination using the mathematics of tangles, a powerful branch of knot theory. Tangle analysis can determine the topology and infer the geometry of DNA undergoing recombination. Apart from the recombination systems investigated in this proposal, the tangle-analysis tools that we develop will be extended to other recombinases and used to investigate related systems such as topoisomerases.